In the given electrical circuit,if the switch | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Initially,when the switch $S$ is open,the two capacitors are charged with $Q_1 = 4 	ext{ C}$ and $Q_2 = 2 	ext{ C}$ respectively. The total init

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(A) Initially,when the switch $S$ is open,the two capacitors are charged with $Q_1 = 4 	ext{ C}$ and $Q_2 = 2 	ext{ C}$ respectively. The total initial energy $E_i$ stored in the capacitors is given by:$E_i = \frac{Q_1^2}{2C_1} + \frac{Q_2^2}{2C_2} = \frac{4^2}{2 	imes 1} + \frac{2^2}{2 	imes 2} = \frac{16}{2} + \frac{4}{4} = 8 	ext{ J} + 1 	ext{ J} = 9 	ext{ J}$.When the switch $S$ is closed,the capacitors are connected in parallel. The common potential $V$ is given by:$V = \frac{Q_1 + Q_2}{C_1 + C_2} = \frac{4 + 2}{1 + 2} = \frac{6}{3} = 2 	ext{ V}$.The final energy $E_f$ stored in the capacitors is:$E_f = \frac{1}{2} (C_1 + C_2) V^2 = \frac{1}{2} (1 + 2) (2)^2 = \frac{1}{2} 	imes 3 	imes 4 = 6 	ext{ J}$.By the law of conservation of energy,the energy lost by the capacitors is stored in the inductor as magnetic energy $E_L$:$E_L = E_i - E_f = 9 	ext{ J} - 6 	ext{ J} = 3 	ext{ J}$.

In the given electrical circuit,if the switch $S$ is closed,then the maximum energy stored in the inductor is: (in $J$)

Similar Questions

$A$ spherical shell of radius $6 \ cm$ is placed concentrically with a sphere of radius $4 \ cm$. The outer spherical shell is grounded. If the potential of the inner sphere is $3 \ e.s.u.$,what is the charge on it in $e.s.u.$?

Find the ratio $\frac{C_{DE}}{C_{AB}}$ for the given circuit.

For the given circuit,find the charge on the $4\ \mu F$ capacitor in $\mu C$.

$A$ conducting sphere $A$ of radius $a$,with charge $Q$,is placed concentrically inside a conducting shell $B$ of radius $b$. $B$ is earthed. $C$ is the common centre of the $A$ and $B$.

Find the charge on capacitor $C_3$. Given that $C_1 = C_2 = C$ and $C_3 = C_4 = 3C$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module